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spayn [35]
3 years ago
13

Prove that the diagonals of a rhombus are perpendicular using coordinate geometry

Mathematics
1 answer:
lozanna [386]3 years ago
5 0

If we draw a rhombus OABC on a coordinate grid with one vertex at the point O (0,0)

and let its height be 1 then (using the Pythagoras theorem) the coordinates of the 4 points will be as follows:-

O = (0,0) , A = (1, 1), B = (sqrt2+ 1 , 1) , C = (sqrt2, 0)

Slope of the diagonal OB = 1 / (sqrt2 + 1)

Slope of the other diagonal AC = - 1 / (sqrt2 - 1)

Product of the slopes = - 1 / ( sqrt2 + 1)(sqrt2 - 1) = -1 / 1 = -1

This proves that the diagonals are perpendicular.

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3 years ago
What is the slope of the line that passes through the points (4, 9) and (1, 6)?
Aleksandr [31]

a = ( 1 , 6 )

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slope =  \frac{y(b) - y(a)}{x(b) - x(a)} \\

Now just need to put the coordinates in the above equation :

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5 0
3 years ago
X-3y-7=0 , 3x-3y-15=0 solve this using cross multiplication​
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Answer:

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Substituting (3) into (1),

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According to (3) and (4),

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I need help with part b and c
Vikki [24]

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